Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cos x}{(1+\cos x)} d x=?$ A. $\mathrm{x}+\tan \frac{\mathrm{x}}{2}+\mathrm{C}$ B. $-\mathrm{x}+\tan \frac{\mathrm{x}}{2}+\mathrm{C}$ C. $\mathrm{x}-\tan \frac{\mathrm{x}}{2}+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{e^{x}} d x=?$ A. $\sqrt{\mathrm{e}^{\mathrm{x}}}+\mathrm{C}$ B. $2 \sqrt{e^{x}}+C$ C. $\frac{1}{2} \sqrt{\mathrm{e}^{\mathrm{x}}}+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int\left\{\frac{1-\tan \left(\frac{x}{2}\right)}{1+\tan \left(\frac{x}{2}\right)}\right\} d x=?$ A. $2 \log \left|\sec \frac{x}{2}\right|+C$ B. $2 \log \left|\cos \frac{x}{2}\right|+C$ C. $2 \log \left|\sec \left(\frac{\pi}{4}-\frac{x}{2}\right)\right|+C$ D. $2 \log \left|\cos \left(\frac{\pi}{4}-\frac{x}{2}\right)\right|+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{(1-\cos x)}=?$ A. $\frac{1}{(x-\sin x)}+C$ B. $\log |x-\sin x|+C$ C. $\log \left|\tan \frac{x}{2}\right|+C$ D. $-\cot \frac{x}{2}+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{(1+\cos x)}=?$ A. $\frac{1}{2} \tan \frac{x}{2}+C$ B. $-\cot \frac{x}{2}+C$ C. $\tan \frac{x}{2}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin x}{(1-\sin x)} d x=?$ A. $-x+\sec x-\tan x+C$ B. $x+\cos x-\sin x+C$ C. $-\log |1-\sin x|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin x}{(1+\sin x)} d x=?$ A. $x+\tan x-\sec x+C$ B. $x-\tan x-\sec x+C$ C. $x-\tan x+\sec x+C$ D. none of these Solution: So,...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{(1+\sin x)}=?$ A. $\tan x+\sec x+C$ B. $\tan x-\sec x+C$ C. $\frac{1}{2} \tan \frac{x}{2}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{1}{(\sqrt{x}+x)} d x=?$ A. $\log |1+\sqrt{x}|+C$ B. $2 \log |1+\sqrt{\mathrm{x}}|+\mathrm{C}$ C. $\frac{1}{\sqrt{x}} \tan ^{-1} \sqrt{x}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(e^{x}-1\right)}=?$ A. $\log \left|e^{x}-1\right|+C$ B. $\log \left|1-e^{-x}\right|+C$ C. $\log \left|e^{x}-1\right|+C$ D. none of these Solution: Given $=$...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{2^{x}}{1-4^{x}} d x=?$ A. $\sin ^{-1}\left(2^{x}\right)+C$ B. $\left(\log e^{2}\right) \sin ^{-1}\left(2^{x}\right)+C$ C. $\left(\log e^{2}\right) \cos ^{-1}\left(2^{x}\right)+C$ D. $\log _{2}$ e) $\sin ^{-1}\left(2^{x}\right)+C$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(e^{x}+e^{-x}\right)}=?$ A. $\cot -1\left(e^{x}\right)+C$ B. $\tan -1\left(e^{x}\right)+C$ C. $\log \left|e^{x}+1\right|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)} d x=?$ A. $\tan \left(x e^{x}\right)+C$ B. $\cot \left(x e^{x}\right)+C$ C. $e^{x} \tan x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}} \mathrm{dx}=?$ A. $\sin ^{-1} \mathrm{x}+\mathrm{C}$ B. $\sin ^{-1} \sqrt{\mathrm{x}}+\mathrm{C}$ C. $\sqrt{1-\mathrm{x}^{2}}+\mathrm{C}$ D. $-\sqrt{1-x^{2}}+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{e^{x}}{\sqrt{1+e^{x}}} d x=?$ A. $2 \sqrt{1+\mathrm{e}^{\mathrm{x}}}+\mathrm{C}$ B. $\frac{1}{2} \sqrt{1+e^{x}}+C$ C. $\frac{1}{\sqrt{1+\mathrm{e}^{x}}}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x} \cot \left(e^{x}\right) d x=?$ A. $\cot \left(e^{x}\right)+C$ B. $\log \left|\sin e^{x}\right|+C$ c. $\log \left|\operatorname{cosec} e^{x}\right|+c$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\tan (\log x)}{x} d x=?$ A. $x \tan (\log x)+C$ B. $\log |\tan x|+C$ C. $\log |\cos (\log x)|+C$ D. $-\log |\cos (\log x)|+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\tan \left(\sin ^{-1} x\right)}{\sqrt{1-x^{2}}} d x=?$ A. $\log \left|\sec \left(\sin ^{-1} x\right)\right|+C$ B. $\log \left|\cos \left(\sin ^{-1} x\right)\right|+C$ C. $\tan \left(\sin ^{1} x\right)+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \operatorname{cosec}^{3}(2 x+1) \cot (2 x+1) d x=?$ A. $\frac{1}{4} \operatorname{cosec}^{4}(2 x+1)+C$ B. $-\frac{1}{3} \operatorname{cosec}^{3}(2 \mathrm{x}+1)+\mathrm{C}$ C. $-\frac{1}{6} \operatorname{cosec}^{3}(2 \mathrm{x}+1)+\mathrm{C}$ D. $\frac{1}{2} \operatorname{cosec}(2 x+1) \cot (2 x+1)+C$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sec ^{5} x \tan x \mathrm{dx}=?$ A. $5 \tan ^{5} x+C$ B. $\frac{1}{5} \tan ^{5} \mathrm{x}+\mathrm{C}$ C. $5 \log |\cos x|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{x^{2} \tan ^{-1} x^{3}}{\left(1+x^{6}\right)} d x=?$ A. $\frac{1}{3}\left(\tan ^{-1} \mathrm{x}^{3}\right)+\mathrm{C}$ B. $\log \left|\tan ^{-1} x^{3}\right|+C$ C. $\frac{1}{6}\left(\tan ^{-1} \mathrm{x}^{3}\right)^{2}+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{1}{x \cos ^{2}(1+\log x)} d x=?$ A. $\tan (1+\log x)+C$ B. $\cot (1+\log x)+C$ C. $\sec (1+\log x)+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cot x}{\log (\sin x)} d x=?$ A. $\log |\cot x|+C$ B. $\log |\cot x \operatorname{cosec} x|+C$ C. $\log |\log \sin x|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{1}{\left(1+x^{2}\right) \sqrt{\tan ^{-1} x}}$ A. $\frac{1}{2} \log \left|\tan ^{-1} x\right|+C$ B. $2 \sqrt{\tan ^{-1} \mathrm{x}}+\mathrm{C}$ C. $\frac{1}{2 \sqrt{\tan ^{-1} x}}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int(\sqrt{\sin x}) \cos x d x=?$ A. $\frac{2}{3}(\cos x)^{3 / 2}+C$ B. $\frac{3}{2}(\cos x)^{3 / 2}+C$ C. $\frac{2}{3}(\sin x)^{3 / 2}+C$ D. $\frac{3}{2}(\sin x)^{3 / 2}+C$ Solution:...
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